Question 238: Gravitation

Question

A simple pendulum is placed at a place where its distance from the earth's surface is equal to the radius of the earth. If the length of the string is $$4 m$$, then the time period of small oscillations will be __________ s. [take $$g=\pi^2 m s^{-2}$$]

Accepted Answer

Acceleration due to gravity g' $$=\frac{g}{4}$$
$$\begin{aligned}
& \mathrm{T}=2 \pi \sqrt{\frac{4 \ell}{\mathrm{g}}} \
& \mathrm{T}=2 \pi \sqrt{\frac{4 	imes 4}{\mathrm{~g}}} \
& \mathrm{~T}=2 \pi \frac{4}{\pi}=8 \mathrm{~s}
\end{aligned}$$

Gravitation

A simple pendulum is placed at a place where its distance from the earth's surface is equal to the radius of the earth. If the length of the string is $4 m, then the time period of small oscillations will be __________ s. [take g=\pi^2 m s^{-2}$]

Integer / Numeric Answer Type